2 Compression Seals,
1 Translocation Seal, can sense dungeon stairs
The Tinker is a rather unconventional class. Not possessing any combat prowess, the Tinker relies on items to provide leverage. By that logic, the Tinker also requires gold to be effective. Dungeons with multiple bosses work in advantage for the Tinker, as they drop large amounts of gold for you to use. The Gloves of Midas is an excellent item to prep with the Tinker, for obvious reasons.
The ability, which allows you to sense subdungeon stairs is very useful. If a Tinker can find Good Glenrick, it equals an easy boost to level 4. A Smuggler's Den subdungeon means a stronger early game for the Tinker. Secret subdungeons are never truly inaccessable to the Tinker, thanks to his Transmutation Seals. Almost all secret subdungeons are beneficial, which is something that the Tinker should never fail to leverage.
There is no particular God that the Tinker requires to worship to be successful, but Tikki Tooki works best for the Tinker, due to the free gold you receive with Tikki's boons. If you're worshipping Tikki, consider an offensive build, so you can conserve piety.
The Tinker's potential increases as you unlock items, especially the Elite items from Bezar. Elite items cost a large amount of gold, but the Tinker comes with a free Translocation Seal, which is essentially a free item. A free Amulet of Yendor can mean an easy win.
The Tinker works with just about any race (except possibly Goblins), although you will need to have a certain strategy in mind, whether it's building a combat-oriented class for humans and orcs, glyph-based class with elves or gnomes, or abusing the Trisword or Alchemist Scroll with Halfling and Gnomes. All in all, the Tinker's a rather luck-based class, but making the most out of the RNG is what Desktop Dungeons is all about. A properly equipped (and slightly lucky) Tinker can clear even Vicious Gaan-Telet with relative ease.